Feng Qi and Jia-Qiang Mei

Abstract: In the article, many inequalities of the integrals $$ \int_x^\infty {\rm e}^{-t^p}dt, \qquad \int_0^x {\rm e}^{-t^p}dt, \qquad \int_0^x {\rm e}^{t^p}dt $$ for $p > 0$, which are related to the incomplete gamma function, are established. The approach used in the paper could yield more particular inequalities of the above functions. Some known results are generalized, extended or refined.